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A comparison of alternative unit root tests

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Author Info
George Halkos
Ilias Kevork

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Abstract

In this paper we evaluate the performance of three methods for testing the existence of a unit root in a time series, when the models under consideration in the null hypothesis do not display autocorrelation in the error term. In such cases, simple versions of the Dickey-Fuller test should be used as the most appropriate ones instead of the known augmented Dickey-Fuller or Phillips-Perron tests. Through Monte Carlo simulations we show that, apart from a few cases, testing the existence of a unit root we obtain actual type I error and power very close to their nominal levels. Additionally, when the random walk null hypothesis is true, by gradually increasing the sample size, we observe that p-values for the drift in the unrestricted model fluctuate at low levels with small variance and the Durbin-Watson (DW) statistic is approaching 2 in both the unrestricted and restricted models. If, however, the null hypothesis of a random walk is false, taking a larger sample, the DW statistic in the restricted model starts to deviate from 2 while in the unrestricted model it continues to approach 2. It is also shown that the probability not to reject that the errors are uncorrelated, when they are indeed not correlated, is higher when the DW test is applied at 1% nominal level of significance. † Email: kevork@uth.gr

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Article provided by Taylor and Francis Journals in its journal Journal of Applied Statistics.

Volume (Year): 32 (2005)
Issue (Month): 1 (January)
Pages: 45-60
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Handle: RePEc:taf:japsta:v:32:y:2005:i:1:p:45-60

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Related research
Keywords: Unit root tests; type I error; power of the test; Monte Carlo simulations;

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References listed on IDEAS
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. George E. Halkos & Ilias S. Kevork, 2006. "Forecasting the stationary AR(1) with an almost unit root," Applied Economics Letters, Taylor and Francis Journals, vol. 13(12), pages 789-793, October. [Downloadable!] (restricted)
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